From f2e04d75257b6158e20963d89dddbb46dbbac3de Mon Sep 17 00:00:00 2001
From: Allaun Silverfox <28494262+allaunthefox@users.noreply.github.com>
Date: Sat, 16 May 2026 13:18:08 -0500
Subject: [PATCH] Document empirical Hessian receipt pass

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+# Empirical Hessian Receipt Pass
+
+## Purpose
+
+This implementation turns the Hessian-basis recompute from a heuristic routing table into measured curvature receipts.
+
+It uses `hessian-eigenthings` as the matrix-free curvature backend. The project rule is:
+
+```text
+do not materialize the full Hessian;
+query directional pressure via HVP/matvec;
+emit receipts for stiffness, flatness, saddle risk, and residual quality.
+```
+
+## Added files
+
+| Path | Purpose |
+|---|---|
+| `5-Applications/tools-scripts/famm/hessian_receipt_runner.py` | CLI receipt runner around `hessian-eigenthings`. |
+| `shared-data/schemas/famm_hessian_curvature_receipt.schema.json` | Receipt schema. |
+| `shared-data/examples/famm_hessian_receipt_config.example.json` | Smoke-test config using a diagonal operator. |
+
+## Route rule
+
+The receipt runner maps measured curvature into route actions:
+
+| Curvature signal | Route action |
+|---|---|
+| negative eigenvalues | `probe_saddle_scar` |
+| dominant eigenvalue above threshold | `protect_or_seal_stiff_invariant` |
+| enough near-zero eigenvalues | `press_flat_gauge` |
+| high trace | `seal_high_total_curvature` |
+| otherwise | `continue_measured_probe` |
+
+## Command
+
+```bash
+pip install hessian-eigenthings
+
+python3 5-Applications/tools-scripts/famm/hessian_receipt_runner.py \
+  --config shared-data/examples/famm_hessian_receipt_config.example.json \
+  --out shared-data/hessian-receipts/example_receipt.json
+```
+
+## Receipt role
+
+The output is not a proof. It is a computational witness that can update:
+
+```text
+proof priority
+compression priority
+scar-probe priority
+closure priority
+```
+
+## No-drift boundary
+
+A Hessian receipt can route work, rank scars, and justify pressure gates. It cannot replace exact Lean/Fraction/OISC proof receipts.